Abstract In classical general relativity, the values of fields on spacetime are uniquely determined by their at an initial time within domain dependence this data surface. However, it may occur that under consideration extends beyond dependence, and fields, therefore, not entirely data. This occurs, for example, in well-known (maximally) extended Reissner–Nordström or Reissner–Nordström–deSitter (RNdS) spacetimes. The boundary region is called ‘Cauchy horizon.’ It located inside black hole...

We introduce a bilinear form for Weyl scalar perturbations of Kerr. The is symmetric and conserved, we show that, when combined with suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the different (l, m, n). These properties apparently not evident consequences standard radial angular solutions to decoupled Teukolsky relations rely on Petrov type D character Kerr its t-$\phi$ reflection isometry. that mode excitation...

We develop a relativistic perturbation theory for scalar clouds around rotating black holes. first introduce product and corresponding orthogonality relation between modes, extending recent result gravitational perturbations. then derive the analog of time-dependent in quantum mechanics, apply it to calculate self-gravitational frequency shifts. This approach supersedes nonrelativistic "gravitational atom" approximation, brings close agreement with numerical relativity, has practical...

We propose a new formula for the entropy of dynamical black hole—valid to leading order perturbations off stationary hole background—in an arbitrary classical diffeomorphism covariant Lagrangian theory gravity in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>n</a:mi></a:math> dimensions. In eras, this agrees with usual Noether charge formula, but nonstationary we obtain nontrivial correction term. particular, general relativity, our differs from standard...

We derive hamiltionian generators of asymptotic symmetries for general relativity with AdS boundary conditions using the ``covariant phase space'' method Wald et al. then compare our results other definitions that have been proposed in literature. find definition agrees by Ashtekar al, spinor definition, and background dependent Henneaux Teitelboim. Our disagrees one obtained from ``counterterm subtraction method,'' but difference is found to consist only a ``constant offset'' determined...

We review uniqueness theorems as well other general results about higher dimensional black hole spacetimes. This includes in particular the topology of spacetimes, their symmetries (rigidity theorem), and classification supersymmetric holes. outline basic ideas underlying proofs these statements, we also indicate ways to generalize some more contexts, such complicated theories.

We consider the memory effect in even dimensional spacetimes of dimension d ≥ 4 arising from a burst gravitational radiation.When = 4, natural frames stationary eras before and after differ by composition boost supertranslation, this supertranslation characterizes "memory effect," i.e., permanent displacement test particles near infinity produced radiation burst.However, we show that when > corresponding vanish.Consequently, it is to impose stronger asymptotic conditions at null reduce...

We investigate the second law of black hole mechanics in gravitational theories with higher derivative terms action. Wall has described a method for defining an entropy that satisfies to linear order perturbations around stationary hole. show this can be extended define quadratic perturbations, provided one treats sense effective field theory. also address some outstanding issues Wall's method, particular, its gauge invariance and relation Iyer-Wald entropy.

We further explore the counterterm subtraction definition of charges (e.g., energy) for classical gravitating theories in spacetimes relevance to gauge/gravity dualities; i.e., asymptotically anti-de Sitter (AdS) spaces and their kin. In particular, we show general that defined via method generate desired asymptotic symmetries. As a result, they can differ from any other such charges, as those by bulk spacetime-covariant techniques, only function auxiliary nondynamical structures choice...

We study the linear stability of asymptotically anti-de Sitter black holes in general relativity spacetime dimension . Our approach is an adaptation framework Hollands and Wald, which gives a criterion terms sign canonical energy, The was originally formulated for static or stationary axisymmetric flat case, analysis that case applies only to perturbations. However, requires hole have single Killing field normal horizon there are no restrictions on perturbations (apart from smoothness...