Papers by Cristian Vicente Menjívar Martínez
Physical Review D, 2007
We consider an action for an abelian gauge field for which the density is given by a power of the... more We consider an action for an abelian gauge field for which the density is given by a power of the Maxwell Lagrangian. In d spacetime dimensions this action is shown to enjoy the conformal invariance if the power is chosen as d/4. We take advantage of this conformal invariance to derive black hole solutions electrically charged with a purely radial electric field. Because of considering power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression of the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordström field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.
Physical Review D, 2004
An exact four-dimensional black hole solution of gravity with a minimally coupled self-interactin... more An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfied on and outside the event horizon. The thermodynamical analysis shows the existence of a critical temperature, below which a black hole in vacuum undergoes a spontaneous dressing up with a nontrivial scalar field in a process reminiscent of ferromagnetism.
Journal of High Energy Physics, 2002
A class of black objects which are solutions of pure gravity with negative cosmological constant ... more A class of black objects which are solutions of pure gravity with negative cosmological constant are classified through the mapping between the Killing spinors of the ground state and those of the transverse section. It is shown that these geometries must have transverse sections of constant curvature for spacetime dimensions d below seven. For d ≥ 7, the transverse sections can also be Euclidean Einstein manifolds. In even dimensions, spacetimes with transverse section of nonconstant curvature exist only in d = 8 and 10. This classification goes beyond standard supergravity and the eleven dimensional case is analyzed. It is shown that if the transverse section has negative scalar curvature, only extended objects can have a supersymmetric ground state. In that case, some solutions are explicitly found whose ground state resembles a wormhole.

Journal of High Energy Physics, 2012
Scalar fields minimally coupled to General Relativity in three dimensions are considered. For cer... more Scalar fields minimally coupled to General Relativity in three dimensions are considered. For certain families of self-interaction potentials, new exact solutions describing solitons and hairy black holes are found. It is shown that they fit within a relaxed set of asymptotically AdS boundary conditions, whose asymptotic symmetry group coincides with the one for pure gravity and its canonical realization possesses the standard central extension. Solitons are devoid of integration constants and their (negative) mass, fixed and determined by nontrivial functions of the self-interaction couplings, is shown to be bounded from below by the mass of AdS spacetime. Remarkably, assuming that a soliton corresponds to the ground state of the sector of the theory for which the scalar field is switched on, the semiclassical entropy of the corresponding hairy black hole is exactly reproduced from Cardy formula once nonvanishing lowest eigenvalues of the Virasoro operators are taking into account, being precisely given by the ones associated to the soliton. This provides further evidence about the robustness of previous results, for which the ground state energy instead of the central charge appears to play the leading role in order to reproduce the hairy black hole entropy from a microscopic counting.

Journal of High Energy Physics, 2011
General Relativity coupled to a self-interacting scalar field in three dimensions is shown to adm... more General Relativity coupled to a self-interacting scalar field in three dimensions is shown to admit exact analytic soliton solutions, such that the metric and the scalar field are regular everywhere. Since the scalar field acquires slow fall-off at infinity, the soliton describes an asymptotically AdS spacetime in a relaxed sense as compared with the one of Brown and Henneaux. Nevertheless, the asymptotic symmetry group remains to be the conformal group, and the algebra of the canonical generators possesses the standard central extension. For this class of asymptotic behavior, the theory also admits hairy black holes which raises some puzzles concerning an holographic derivation of their entropyà la Strominger. Since the soliton is devoid of integration constants, it has a fixed (negative) mass, and it can be naturally regarded as the ground state of the "hairy sector", for which the scalar field is switched on. This assumption allows to exactly reproduce the semiclassical hairy black hole entropy from the asymptotic growth of the number of states by means of Cardy formula. Particularly useful is expressing the asymptotic growth of the number of states only in terms of the spectrum of the Virasoro operators without making any explicit reference to the central charges.

Physical Review D, 2010
Recently, the asymptotic behaviour of three-dimensional anti-de Sitter gravity with a topological... more Recently, the asymptotic behaviour of three-dimensional anti-de Sitter gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two-dimensional conformal group and that included a fall-off of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp-waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely the chirality that has the milder behaviour at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast, both chiralities are subdominant with respect to the asymptotic behaviour of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).

Physical Review D, 2011
Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological ... more Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the "massive graviton") is switched on. An exact solution with this property is explicitly exhibited and possesses a slower fall-off than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra. We show that the canonical generators are integrable and finite. When the graviton is not excited, our analysis is compared and contrasted with earlier results obtained through the covariant approach to conserved charges. In particular, we find agreement with the conserved charges of the warped AdS black holes as well as with the central charges in the algebra.

Physical Review D, 2006
An electrically charged black hole solution with scalar hair in four dimensions is presented. The... more An electrically charged black hole solution with scalar hair in four dimensions is presented. The self-interacting scalar field is real and it is minimally coupled to gravity and electromagnetism. The event horizon is a surface of negative constant curvature and the asymptotic region is locally an AdS spacetime. The asymptotic fall-off of the fields is slower than the standard one. The scalar field is regular everywhere except at the origin, and is supported by the presence of electric charge which is bounded from above by the AdS radius. In turn, the presence of the real scalar field smooths the electromagnetic potential everywhere. Regardless the value of the electric charge, the black hole is massless and has a fixed temperature. The entropy follows the usual area law. It is shown that there is a nonvanishing probability for the decay of the hairy black hole into a charged black hole without scalar field. Furthermore, it is found that an extremal black hole without scalar field is likely to undergo a spontaneous dressing up with a nontrivial scalar field, provided the electric charge is below a critical value.
Physical Review D, 2005
It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlin... more It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlinear Klein-Gordon equation without curving spacetime. Surprisingly, this possibility arises from the nonminimal coupling of the scalar field with the curvature, since a footprint of the coupling remains in the energy-momentum tensor even when gravity is switched off. Requiring the existence of solutions with vanishing energy-momentum tensor fixes the selfinteraction potential as a local function of the scalar field depending on two coupling constants. The solutions describe shock waves and, in the Euclidean continuation, instanton configurations in any dimension. As a consequence of this effect, the tachyonic solutions of the free massive Klein-Gordon equation become part of the vacuum.
Physical Review D, 2004
We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound... more We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D ≥ 3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the backreaction of the scalar field, which has a logarithmic branch decreasing as r −(D−1)/2 ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative cosmological constant (conformal group in D − 1 dimensions). The generators of the asymptotic symmetries are finite even when the logarithmic branch is considered but acquire, however, a contribution from the scalar field.
Physical Review D, 1996
A three dimensional black hole solution of Einstein equations with negative cosmological constant... more A three dimensional black hole solution of Einstein equations with negative cosmological constant coupled to a conformal scalar field is given. The solution is static, circularly symmetric, asymptotically anti-de Sitter and nonperturbative in the conformal field. The curvature tensor is singular at the origin while the scalar field is regular everywhere. The condition that the Euclidean geometry be regular at the horizon fixes the temperature to be T = 9 r + 16πl 2. Using the Hamiltonian formulation including boundary terms of the Euclidean action, the entropy is found to be 2 3 of the standard value (1
Physical Review D, 2003
An exact expression for the quasinormal modes of scalar perturbations on a massless topological b... more An exact expression for the quasinormal modes of scalar perturbations on a massless topological black hole in four and higher dimensions is presented. The massive scalar field is nonminimally coupled to the curvature, and the horizon geometry is assumed to have a negative constant curvature.

Physical Review D, 2000
The generalization of the black hole in three-dimensional spacetime to include an electric charge... more The generalization of the black hole in three-dimensional spacetime to include an electric charge Q in addition to the mass M and the angular momentum J is given. The field equations are first solved explicitly when Q is small and the general form of the field at large distances is established. The total "hairs" M, J and Q are exhibited as boundary terms at infinity. It is found that the inner horizon of the rotating uncharged black hole is unstable under the addition of a small electric charge. Next it is shown that when Q = 0 the spinning black hole may be obtained from the one with J = 0 by a Lorentz boost in the ϕ − t plane. This boost is an "illegitimate coordinate transformation" because it changes the physical parameters of the solution. The extreme black hole appears as the analog of a particle moving with the speed of light. The same boost may be used when Q = 0 to generate a solution with angular momentum from that with J = 0,
Physical Review D, 2003
A four-dimensional black hole solution of the Einstein equations with a positive cosmological con... more A four-dimensional black hole solution of the Einstein equations with a positive cosmological constant coupled to a conformal scalar field is given. There is a curvature singularity at the origin, and the scalar field has a divergence inside the event horizon. The electrically charged solution, which has a fixed charge-to-mass ratio, is also found. The quartic self-interacting coupling constant becomes bounded in terms of Newton's constant and the cosmological constant. The solution satisfies both dominant and the strong energy conditions.

Physical Review D, 2003
Three-dimensional gravity with a minimally coupled self-interacting scalar is considered. The fal... more Three-dimensional gravity with a minimally coupled self-interacting scalar is considered. The fall-off of the fields at infinity is assumed to be slower than that of a localized distribution of matter, so that the asymptotic symmetry group is the conformal group. The counterterm Lagrangian needed to render the action finite is found by demanding that the action attain an extremum for the boundary conditions implied by the above fall-off of the fields at infinity. These counterterms explicitly depend on the scalar field. As a consequence, the Brown-York stress-energy tensor acquires a non trivial contribution from the matter sector. Static circularly symmetric solutions with a regular scalar field are explored for a one-parameter family of potentials. Their masses are computed via the Brown-York quasilocal stress-energy tensor, and they coincide with the values obtained from the Hamiltonian approach. The thermal behavior, including the transition between different configurations, is analyzed, and it is found that the scalar black hole can decay into the BTZ solution irrespective of the horizon radius. It is also shown that the AdS/CFT correspondence yields the same central charge as for pure gravity.
General Relativity and Gravitation, 2006
A nontrivial scalar field configuration of vanishing energy-momentum is reported. These matter co... more A nontrivial scalar field configuration of vanishing energy-momentum is reported. These matter configurations have no influence on the metric and therefore they are not be "detected" gravitationally. This phenomenon occurs for a time-dependent nonminimally coupled and self-interacting scalar field on the 2 + 1 (BTZ) black hole geometry. We conclude that such stealth configurations exist for the static 2 + 1 black hole for any value of the nonminimal coupling parameter ζ = 0 with a fixed self-interaction potential U ζ (Φ). For the range 0 < ζ ≤ 1/2 potentials are bounded from below and for the range 0 < ζ < 1/4 the stealth field falls into the black hole and is swallowed by it at an exponential rate, without any consequence for the black hole.

Physical Review D, 2008
We study static, spherically symmetric black hole solutions of the Einstein equations with a posi... more We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self interacting scalar field. Exact solutions for this model found by Martínez, Troncoso, and Zanelli, (MTZ), were subsequently shown to be unstable under linear gravitational perturbations, with modes that diverge arbitrarily fast. We find that the moduli space of static, spherically symmetric solutions that have a regular horizon-and satisfy the weak and dominant energy conditions outside the horizon-is a singular subset of a two dimensional space parameterized by the horizon radius and the value of the scalar field at the horizon. The singularity of this space of solutions provides an explanation for the instability of the MTZ spacetimes, and leads to the conclusion that, if we include stability as a criterion, there are no physically acceptable black hole solutions for this system that contain a cosmological horizon in the exterior of its event horizon.
Mathematische Zeitschrift, 2018
We give further counterexamples to the conjectural construction of Bridgeland stability on threef... more We give further counterexamples to the conjectural construction of Bridgeland stability on threefolds due to Bayer, Macrì, and Toda. This includes smooth projective threefolds containing a divisor that contracts to a point, and Weierstraß elliptic Calabi-Yau threefolds. Furthermore, we show that if the original conjecture, or a minor modification of it, holds on a smooth projective threefold, then the space of stability conditions is non-empty on the blow up at an arbitrary point. More precisely, there are stability conditions on the blow up for which all skyscraper sheaves are semistable.

arXiv (Cornell University), Oct 6, 2019
On a Weierstraß elliptic surface X, we define a 'limit' of Bridgeland stability conditions, denot... more On a Weierstraß elliptic surface X, we define a 'limit' of Bridgeland stability conditions, denoted as Z l-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the polarisation fixed. We describe conditions under which a slope stable torsion-free sheaf is taken by a Fourier-Mukai transform to a Z l-stable object, and describe a modification upon which a Z l-semistable object is taken by the inverse Fourier-Mukai transform to a slope semistable torsion-free sheaf. We also study wall-crossing for Bridgeland stability, and show that 1-dimensional twisted Gieseker semistable sheaves are taken by a Fourier-Mukai transform to Bridgeland semistable objects. CONTENTS 1. Introduction 1 2. Preliminaries 4 3. Constructing a limit Bridgeland stability 12 4. Slope stability vs limit Bridgeland stability 16 5. The Harder-Narasimhan property of limit Bridgeland stability 21 6. Transforms of 1-dimensional sheaves 24 7. Asymptotics for Bridgeland Walls on Weierstraß surfaces 30 8. Transforms of line bundles of fiber degree at least 2 36 Appendix A. Bridgeland wall-chamber structures 38 Appendix B. Potential walls in (λ, 0, 0, q)-plane for one-dimensional objects 43 References 44
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Papers by Cristian Vicente Menjívar Martínez