Static Black Hole Solutions Research Articles

New cylindrical gravitational soliton waves and gravitational Faraday rotation

In terms of gravitational solitons, we study gravitational non-linear effects of gravitational solitary waves such as Faraday rotation. Applying the Pomeransky's procedure for inverse scattering method, which has been recently used for constructing stationary black hole solutions in five dimensions to a cylindrical spacetime in four dimensions, we construct a new cylindrically symmetric soliton solution. This is the first example to be applied to the cylindrically symmetric case. In particular, we clarify the difference from the Tomimatsu's single soliton solution, which was constructed by the Belinsky-Zakharov's procedure.

Analogue black holes for light rays in static dielectrics

Propagation of light in nonlinear materials is here studied in the regime of the geometrical optics. It is shown that a spherically symmetric medium at rest with some specific dielectric properties can be used to produce an exact analogue model for a class of space-times which includes spherically symmetric and static black hole solutions. The optical model here presented can be a useful tool to reproduce in laboratory the behavior of optical null geodesics near a compact object with an observable gravitational Schwarzschild radius.

Stability of black holes and solitons in Anti-de Sitter space-time

The stability of black holes and solitons in d-dimensional Anti-de Sitter (AdSd) space-time against scalar field condensation is discussed. The resulting solutions are “hairy” black holes and solitons, respectively. In particular, we will discuss static black hole solutions with hyperbolic, flat and spherical horizon topology and emphasize that two different type of instabilities exist depending on whether the scalar field is charged or uncharged, respectively. We will also discuss the influence of Gauss-Bonnet curvature terms. The results have applications within the AdS/CFT correspondence and describe e.g. holographic insulator/conductor/superconductor phase transitions.

N = 2 SUGRA BPS multi-center solutions, quadratic prepotentials and Freudenthal transformations

We present a detailed description of N=2 stationary BPS multicenter black hole solutions for quadratic prepotentials with an arbitrary number of centers and scalar fields making a systematic use of the algebraic properties of the matrix of second derivatives of the prepotential, $\mathcal{S}$, which in this case is a scalar-independent matrix. In particular we obtain bounds on the physical parameter of the multicenter solution such as horizon areas and ADM mass. We discuss the possibility and convenience of setting up a basis of the symplectic vector space built from charge eigenvectors of the $\ssigma$, the set of vectors $(\Ppm q_a)$ with $\Ppm$ $\ssigma$-eigenspace proyectors. The anti-involution matrix $\mathcal{S}$ can be understood as a Freudenthal duality $\tilde{x}=\ssigma x$. We show that this duality can be generalized to "Freudenthal transformations" $$x\to \lambda\exp(\theta \ssigma) x= a x+b\tilde{x}$$ under which the horizon area, ADM mass and intercenter distances scale up leaving constant the fix point scalars. In the special case $\lambda=1$, "$\ssigma$-rotations", the transformations leave invariant the solution. The standard Freudental duality can be written as $\tilde x= \exp(\pi/2 \ssigma) x .$ We argue that these generalized transformations leave also invariant the general stringy extremal quartic form $\Delta_4$, $\Delta_4(x)= \Delta_4(\cos\theta x+\sin\theta\tilde{x})$.

Conformally Lifshitz solutions from Horava–Lifshitz Gravity

We show that the IR action of the healthy non-projectable Hořava–Lifshitz gravity and its small modification exhibit Lifshitz and hyperscaling violating solutions, respectively, though it does not have the corresponding static black hole solutions. The model may also have an AdS2 × Rd vacuum solution.

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

We investigate background metrics for 2 + 1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton-York tensor takes the form of the energy-momentum tensor of a perfect fluid, i.e. they are of Petrov type Dt. Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3 + 1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy-momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.

Topological solutions in ungauged supergravity

A new general class of solutions of ungauged four-dimensional Supegravity, in one-to-one correspondence with spherically symmetric, static black-hole solutions and Lifshitz solutions with Hyperscaling violation (\emph{hvLif}) is studied. The causal structure of the space-time is then elucidated.

Null-wave giant gravitons from thermal spinning brane probes

We construct and analyze thermal spinning giant gravitons in type II/M-theory based on spherically wrapped black branes, using the method of thermal probe branes originating from the blackfold approach. These solutions generalize in different directions recent work in which the case of thermal (non-spinning) D3-brane giant gravitons was considered, and reveal a rich phase structure with various new properties. First of all, we extend the construction to M-theory, by constructing thermal giant graviton solutions using spherically wrapped M2- and M5-branes. More importantly, we switch on new quantum numbers, namely internal spins on the sphere, which are not present in the usual extremal limit for which the brane world volume stress tensor is Lorentz invariant. We examine the effect of this new type of excitation and in particular analyze the physical quantities in various regimes, including that of small temperatures as well as low/high spin. As a byproduct we find new stationary dipole-charged black hole solutions in AdS_m X S^n backgrounds of type II/M-theory. We finally show, via a double scaling extremal limit, that our spinning thermal giant graviton solutions lead to a novel null-wave zero-temperature giant graviton solution with a BPS spectrum, which does not have an analogue in terms of the conventional weakly coupled world volume theory.

Scalar, electromagnetic, and gravitational perturbations of Kerr-Newman black holes in the slow-rotation limit

In Einstein-Maxwell theory, according to classic uniqueness theorems, the most general stationary black-hole solution is the axisymmetric Kerr-Newman metric, which is defined by three parameters: mass, spin and electric charge. The radial and angular dependence of gravitational and electromagnetic perturbations in the Kerr-Newman geometry do not seem to be separable. In this paper we circumvent this problem by studying scalar, electromagnetic and gravitational perturbations of Kerr-Newman black holes in the slow-rotation limit. We extend (and provide details of) the analysis presented in a recent Letter [arXiv:1304.1160]. Working at linear order in the spin, we present the first detailed derivation of the axial and polar perturbation equations in the gravito-electromagnetic case, and we compute the corresponding quasinormal modes for any value of the electric charge. Our study is the first self-consistent stability analysis of the Kerr-Newman metric, and in principle it can be extended to any order in the small rotation parameter. We find numerical evidence that the axial and polar sectors are isospectral at first order in the spin, and speculate on the possible implications of this result.

Para-complex geometry and gravitational instantons

We give a complete classification of supersymmetric gravitational instantons in Euclidean N = 2 supergravity coupled to vector multiplets. An interesting class of solutions is found which corresponds to the Euclidean analogue of stationary black hole solutions of N = 2 supergravity theories.

Einstein gravity with Gauss-Bonnet entropic corrections

A toy model of Einstein gravity with a Gauss-Bonnet classically ``entropic'' term mimicking a quantum correction is considered. The static black hole solution due to Tomozawa is found and generalized with the inclusion of nontrivial horizon topology, and its entropy is evaluated, deriving the first law by equations of motion. As a result the Bekenstein-Hawking area law turns out to be corrected by a logarithmic area term. A Misner-Sharp expression for the mass of a black hole is found. Within a Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological setting, the model is used in order to derive modified Friedmann equations. Such new equations are shown to reproduce the first law with the same formal entropy and quasilocal energy of the static case, but here within a Friedmann-Lema\^{\i}tre-Robertson-Walker space-time interpreted as a dynamical cosmological black hole. A detailed analysis of cosmological solutions is presented, and it is shown that the presence of the correction term provides regular solutions and interesting phases of acceleration and deceleration, as well as, with negligible matter, exact de Sitter solutions.

Gravitoelectromagnetic perturbations of Kerr-Newman black holes: stability and isospectrality in the slow-rotation limit.

The most general stationary black-hole solution of Einstein-Maxwell theory in vacuum is the Kerr-Newman metric, specified by three parameters: mass M, spin J, and charge Q. Within classical general relativity, one of the most important and challenging open problems in black-hole perturbation theory is the study of gravitational and electromagnetic fields in the Kerr-Newman geometry, because of the indissoluble coupling of the perturbation functions. Here we circumvent this long-standing problem by working in the slow-rotation limit. We compute the quasinormal modes up to linear order in J for any value of Q and provide the first, fully consistent stability analysis of the Kerr-Newman metric. For scalar perturbations the quasinormal modes can be computed exactly, and we demonstrate that the method is accurate within 3% for spins J/J(max) ≲ 0.5, where J(max) is the maximum allowed spin for any value of Q. Quite remarkably, we find numerical evidence that the axial and polar sectors of the gravitoelectromagnetic perturbations are isospectral to linear order in the spin. The extension of our results to nonasymptotically flat space-times could be useful in the context of gauge-gravity dualities and string theory.

Uniqueness of extreme horizons in Einstein–Yang–Mills theory

We consider stationary extreme black hole solutions to the Einstein–Yang–Mills equations in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS2 symmetry and deduce that its near-horizon geometry must be that of the Abelian embedded extreme Kerr–Newman (AdS) black hole. We also show that the near-horizon geometry of any static black hole is a direct product of AdS2 and a constant curvature space.Communicated by H Reall

Charged black holes in nonlinear massive gravity

We find static charged black hole solutions in nonlinear massive gravity. In the parameter space of two gravitational potential parameters $(\ensuremath{\alpha},\ensuremath{\beta})$ we show that below the Compton wavelength the black hole solutions reduce to that of Reissner-Nordstr\"om via the Vainshtein mechanism in the weak-field limit. In the simplest case with $\ensuremath{\alpha}=\ensuremath{\beta}=0$ the solution exhibits the van Dam-Veltman-Zakharov discontinuity but ordinary general relativity is recovered deep inside the horizon due to the existence of electric charge, though this case is observationally excluded. For $\ensuremath{\alpha}\ensuremath{\ne}0$ and $\ensuremath{\beta}=0$, the post-Newtonian parameter of the charged black hole evolves to that of general relativity via the Vainshtein mechanism within a macroscopic distance; however, a logarithmic correction to the metric factor of the time coordinate is obtained. When $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are both nonzero, there exist two branches of solutions depending on the positivity of $\ensuremath{\beta}$. When $\ensuremath{\beta}<0$, the strong coupling of the scalar graviton weakens gravity at distances smaller than the Vainshtein radius. However, when $\ensuremath{\beta}>0$ the metric factors exhibit only small corrections compared to the solutions obtained in general relativity, and under a particular choice of $\ensuremath{\beta}={\ensuremath{\alpha}}^{2}/6$ the standard Reissner-Nordstr\"om-de Sitter solution is recovered.

Large Randall–Sundrum II black holes

Using a novel numerical spectral method, we have constructed an AdS5–CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci–DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall–Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in 1/(−ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(−Λ).

Holographic renormalization of asymptotically flat gravity

We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \rightarrow \infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.

Topological electro-vacuum solutions in extended gravity

Spherically symmetric static topological black hole solutions associated with some extended higher order gravitational models in the presence of a Maxwell-field are derived by means of simple Lagrangian method, based on spherically symmetric reduction. Some new topological black hole solutions are presented and the validity of the First Law is investigated, and in these cases an expression for the energy is provided.

Static nonextremal AdS4 black hole solutions

We find new static nonextremal black hole solutions that asymptote to AdS4 in D = 4 gauged $ \mathcal{N} $ = 2 supergravity. Solutions include electric and magnetic black holes with constant scalars that in the BPS limit reduce to naked singularities, but also magnetic black holes with running scalars that at extremality reduce to BPS black holes with finite horizon area. For all these solutions we compute area product formulae and show they are independent of the mass. Finally, we also find new examples of nonextremal magnetic black branes.

Black holes and black strings of N = 2, d = 5 supergravity in the H-FGK formalism

We study general classes and properties of extremal and non-extremal static black-hole solutions of N = 2, d = 5 supergravity coupled to vector multiplets using the recently proposed H-FGK formalism, which we also extend to static black strings. We explain how to determine the integration constants and physical parameters of the blackhole and black-string solutions. We derive some model-independent statements, including the transformation of non-extremal flow equations to the form of those for the extremal flow. We apply our methods to the construction of example solutions (among others a new extremal string solution of heterotic string theory on K 3 × S 1). In the cases where we have calculated it explicitly, the product of areas of the inner and outer horizon of a non-extremal solution coincides with the square of the moduli-independent area of the horizon of the extremal solution with the same charges.

Slowly rotating black holes in dynamical Chern-Simons gravity: Deformation quadratic in the spin

We derive a stationary and axisymmetric black hole solution to quadratic order in the spin angular momentum. The previously found, linear-in-spin terms modify the odd-parity sector of the metric, while the new corrections appear in the even-parity sector. These corrections modify the quadrupole moment, as well as the (coordinate-dependent) location of the event horizon and the ergoregion. Although the linear-in-spin metric is of Petrov type D, the quadratic-order terms render it of type I. The metric does not possess a second-order Killing tensor or a Carter-like constant. The new metric does not possess closed timelike curves or spacetime regions that violate causality outside of the event horizon. The new, even-parity modifications to the Kerr metric decay less rapidly at spatial infinity than the leading order in spin, odd-parity ones, and thus, the former are more important when considering black holes that are rotating moderately fast. We calculate the modifications to the Hamiltonian, binding energy and Kepler's third law. These modifications are crucial for the construction of gravitational wave templates for black hole binaries, which will enter at second post-Newtonian order, just like dissipative modifications found previously.