arXiv subjects
Publications and source records attributed to Hari K. Kunduri.
We derive new identities for the thermodynamic variables of five-dimensional, asymptotically flat, stationary and biaxisymmetric vacuum black holes. These identities depend on the topology of the solution and include contributions arising from certain topological charges. The proof employs the harmonic map formulation of the vacuum Einstein equations for solutions with these symmetries.
We prove that any asymptotically flat static spacetime in higher dimensional Einstein-Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black holes in this theory. In particular, these results establish that there are no asymptotically flat static spacetimes with non-trivial topology, with or without a black hole, in Einstein-Maxwell theory.
We examine potential deformations of inner black hole and cosmological horizons in Reissner-Nordström de-Sitter spacetimes. While the rigidity of the outer black hole horizon is guaranteed by theorem, that theorem applies to neither the inner black hole nor past cosmological horizon. Further for pure deSitter spacetime it is clear that the cosmological horizon can be deformed (by translation). For specific parameter choices, it is shown that both inner black hole and cosmological horizons can be infinitesimally deformed. However these do not extend to finite deformations. The corresponding results for general spherically symmetric spacetimes are considered.
In five-dimensional minimal supergravity, there are spherical black holes with nontrivial topology outside the horizon which have the same conserved charges at infinity as the BMPV solution. We show that some of these black holes have greater entropy than the BMPV solution. These spacetimes are all asymptotically flat, stationary, and supersymmetric. We also show that there is a limit in which the black hole shrinks to zero size and the solution becomes a nonsingular "bubbling" geometry. Thus, these solutions provide explicit analytic examples of placing black holes inside solitons.
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles. We discuss how this may lead to a gross violation of black hole uniqueness, beyond the existence of black rings, even for solutions with two commuting rotational symmetries. We illustrate this with a simple example in minimal supergravity; a four parameter family of supersymmetric black hole solutions, with spherical horizon topology and a 2-cycle in the exterior. We show there are black holes in this family with identical conserved changes to the BMPV black hole, thereby demonstrating black hole non-uniqueness in this context. We find a decoupling limit of this family of black holes that yields spacetimes asymptotic to the near-horizon geometry of a BMPV black hole which contain a black hole and an exterior 2-cycle.
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have non-zero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This `first law of black hole and soliton mechanics' contains new intensive and extensive quantities associated to each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulae relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.
We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional U(1)^3-supergravity which is regular on and outside an event horizon of lens space topology L(2,1). The solution has seven independent parameters and uplifts to a family of 1/8-supersymmetric D1-D5-P black brane solutions to Type IIB supergravity. The decoupling limit is asymptotically AdS(3) x S^3 x T^4, with a near-horizon geometry that is a twisted product of the near-horizon geometry of the extremal BTZ black hole and L(2,1) x T^4, although it is not (locally) a product space in the bulk. We show that the decoupling limit of a special case of the black lens is related to that of a black ring by spectral flow, thereby supplying an account of its entropy. Analogous solutions of U(1)^N-supergravity are also presented.
We examine several aspects of black hole horizon physics using the Melvin-Kerr-Newman (MKN) family of spacetimes. Roughly speaking these are black holes immersed in a distorting background magnetic field and unlike the standard Kerr-Newman (KN) family they are not asymptotically flat. As exact solutions with horizons that can be highly distorted relative to KN, they provide a good testbed for ideas about and theorems constraining black hole horizons. We explicitly show that MKN horizons with fixed magnetic field parameter may be uniquely specified by their area, charge and angular momentum and that the charge and angular momentum are bound by horizon area in the same way as for KN. As expected, extremal MKN horizons are geometrically isomorphic to extremal KN horizons and the geometric distortion of near-extremal horizons is constrained by their proximity to extremality. At the other extreme, Melvin-Schwarzschild (MS) solutions may be infinitely distorted, however for intermediate cases any non-zero charge or angular momentum restricts distortions to be finite. These properties are in agreement with known theorems but are seen to be satisfied in interesting and non-trivial ways.
We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, $U(1)^2$-invariant initial data sets on simply connected four dimensional manifolds $Σ$. Moreover, we extend the local mass angular momenta inequality result Ref [1] for $U(1)^2$ invariant black holes to the case with nonzero stress energy tensor with positive matter density and energy-momentum current invariant under the above symmetries.
We revisit the problem of perturbations of Schwarzschild-AdS$_4$ black holes by using a combination of the Martel-Poisson formalism for perturbations of four-dimensional spherically symmetric spacetimes and the Kodama-Ishibashi formalism. We clarify the relationship between both formalisms and express the Brown-York-Balasubramanian-Krauss boundary stress-energy tensor, $\bar{T}_{μν}$, on a finite-$r$ surface purely in terms of the even and odd master functions. Then, on these surfaces we find that the spacelike components of the conservation equation $\bar{\mathcal{D}}^μ\bar{T}_{μν} =0$ are equivalent to the wave equations for the master functions. The renormalized stress-energy tensor at the boundary $\displaystyle \frac{r}{L} \lim_{r \rightarrow \infty} \bar{T}_{μν}$ is calculated directly in terms of the master functions.
We consider initial data for extreme vacuum asymptotically flat black holes with $\mathbb{R} \times U(1)^2$ symmetry. Such geometries are critical points of a mass functional defined for a wide class of asymptotically flat, `$(t-ϕ^i)$' symmetric maximal initial data for the vacuum Einstein equations. We prove that the above extreme geometries are local minima of mass amongst nearby initial data (with the same interval structure) with fixed angular momenta. Thus the ADM mass of nearby data $m\geq f(J_1,J_2)$ for some function $f$ depending on the interval structure. The proof requires that the initial data of the critical points satisfy certain conditions that are satisfied by the extreme Myers-Perry and extreme black ring data.
We consider a broad class of asymptotically flat, maximal initial data sets satisfying the vacuum constraint equations, admitting two commuting rotational symmetries. We construct a mass functional for `$t-ϕ^i$' symmetric data which evaluates to the ADM mass. We then show that $\mathbb{R} \times U(1)^2$-invariant solutions of the vacuum Einstein equations are critical points of this functional amongst this class of data. We demonstrate positivity of this functional for a class of rod structures which include the Myers-Perry initial data. The construction is a natural extension of Dain's mass functional to $D=5$, although several new features arise.
We present a new infinite class of near-horizon geometries of degenerate horizons, satisfying Einstein's equations for all odd dimensions greater than five. The symmetry and topology of these solutions is compatible with those of black holes. The simplest examples give horizons of spatial topology S^3xS^2 or the non-trivial S^3-bundle over S^2. More generally, the horizons are Lens space bundles associated to certain principal torus-bundles over Fano Kaehler-Einstein manifolds. We also consider the classification problem for Einstein metrics on such Lens space bundles and derive a family which unifies all the known examples (Sasakian and non-Sasakian).
We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens space topology L(2,1). It is the first example of an asymptotically flat black hole with lens space topology. The solution is characterised by a charge, two angular momenta and a magnetic flux through a non-contractible disc region ending on the horizon, with one constraint relating these.
We consider maximal slices of the Myers-Perry black hole, the doubly spinning black ring, and the Black Saturn solution. These slices are complete, asymptotically flat Riemannian manifolds with inner boundaries corresponding to black hole horizons. Although these spaces are simply connected as a consequence of topological censorship, they have non-trivial topology. In this note we investigate the question of whether the topology of spatial sections of the horizon uniquely determines the topology of the maximal slices. We show that the horizon determines the homological invariants of the slice under certain conditions. The homological analysis is extended to black holes for which explicit geometries are not yet known. We believe that these results could provide insights in the context of proving existence of deformations of this initial data. For the topological slices of the doubly spinning black ring and the Black Saturn we compute the homotopy groups up to dimension 3 and show that their 4-dimensional homotopy group is not trivial.
We derive a mass formula and a mass variation law for asymptotically flat, stationary spacetimes, invariant under two commuting rotational symmetries, in a general five dimensional theory of gravity coupled to an arbitrary set of Maxwell fields and uncharged scalar fields. If the spacetime is everywhere regular, these mass formulas reduce to a sum of magnetic flux terms defined on its non-trivial 2-cycles. If there is a black hole, we obtain a mass variation law more general than previously obtained, which also has contributions from the 2-cycles exterior to the black hole. This can be interpreted as the first law of black hole mechanics in a background soliton containing bubbles.
Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.
We point out a simple construction of an infinite class of Einstein near-horizon geometries in all odd dimensions greater than five. Cross-sections of the horizons are inhomogeneous Sasakian metrics (but not Einstein) on S^3xS^2 and more generally on Lens space bundles over any compact positive Kaehler-Einstein manifold. They are all consistent with the known topology and symmetry constraints for asymptotically flat or globally AdS black holes.