In this paper we discuss the uniqueness of supersymmetric attractors in four dimensional N = 2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness.

We find the membrane equations which describe the leading order in 1/D dynamics of black holes in the D → ∞ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor for the membrane whose conservation gives the membrane equations. We apply the membrane equations to predict the light quasi-normal mode spectrum of black holes and black branes in the theory of gravity under consideration.

We study the effect of Freudenthal duality on supersymmetric extremal black hole attractors in N = 2, D = 4 ungauged supergravity. Freudenthal duality acts on the dyonic black hole charges as an anti-involution which keeps the black hole entropy and the critical points of the effective black hole potential invariant. We analyze its effect on the recently discovered distinct, mutually exclusive phases of axionic supersymmetric black holes, related to the existence of non-trivial involutory constant matrices. In particular, we consider a supersymmetric D0 − D4 − D6 black hole and we explicitly Freudenthal-map it to a supersymmetric D0 − D2 − D4 − D6 black hole. We thus show that the charge representation space of a supersymmetric D0 − D2 − D4 − D6 black hole also contains mutually exclusive domains.

In this paper we study spherically symmetric single-centered attractors in N = 2 supergravity in four dimensions. The attractor points are obtained by extremising the effective black hole potential in the moduli space. Both supersymmetric as well as non-supersymmetric attractors exist in mutually exclusive domains of the charge lattice. We construct axion free supersymmetric as well as non-supersymmetric multiple attractors in a simple two parameter model. We further obtain explicit examples of two distinct nonsupersymmetric attractors in type IIA string theory compactified on K3 × T 2 carrying D0 − D4 − D6 charges. We compute the entropy of these attractors and analyse their stability in detail.

Two derivative Jackiw-Teitelboim (JT) gravity theory captures the near-horizon dynamics of higher dimensional near-extremal black holes, which is governed by a Schwarzian action at the boundary in the near-horizon region. The partition function corresponding to this boundary action correctly gives the statistical entropy of the near-extremal black hole. In this paper, we study the thermodynamics of spherically symmetric four-dimensional near-extremal black holes in presence of arbitrary perturbative four derivative corrections. We find that the near-horizon dynamics is again captured by a JT-like action with a particular namely R2 higher derivative modification. Effectively the theory is described by a boundary Schwarzian action which gets suitably modified due to the presence of the higher derivative interactions. Near-extremal entropy, free energy also get corrected accordingly.