Carlos Herdeiro

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Kerr black holes with scalar hair.

We present a family of solutions of Einsteins gravity minimally coupled to a complex, massive scalar field, describing asymptotically flat, spinning black holes with scalar hair and a regular horizon. These hairy black holes (HBHs) are supported by rotation and have no static limit. Besides mass M and angular momentum J, they carry a conserved, continuous Noether charge Q measuring the scalar hair. HBHs branch off from the Kerr metric at the threshold of the superradiant instability and reduce to spinning boson stars in the limit of vanishing horizon area. They overlap with Kerr black holes for a set of (M, J) values. A single Killing vector field preserves the solutions, tangent to the null geodesic generators of the event horizon. HBHs can exhibit sharp physical differences when compared to the Kerr solution, such as J/M^{2}>1, a quadrupole moment larger than J^{2}/M, and a larger orbital angular velocity at the innermost stable circular orbit. Families of HBHs connected to the Kerr geometry should exist in scalar (and other) models with more general self-interactions.

D3 / D7 inflationary model and M theory

A proposal is made for a cosmological D3-D7 model with a constant magnetic flux along the D7 world volume. It describes an

Asymptotically flat black holes with scalar hair: a review

\mathcal{N}=2

Construction and physical properties of Kerr black holes with scalar hair

gauge model with Fayet-Iliopoulos terms and the potential of the hybrid P-term inflation. The motion of the D3-brane towards D7 in a phase with spontaneously broken supersymmetry provides a period of slow-roll inflation in the de Sitter valley, the role of the inflaton being played by the distance between D3- and D7-branes. After tachyon condensation a supersymmetric ground state is formed: a D3-D7 bound state corresponding to an Abelian non-linear (non-commutative) instanton. In this model the existence of a non-vanishing cosmological constant is associated with the resolution of the instanton singularity. We discuss a possible embedding of this model into a compactified M-theory setup.

Shadows of Kerr black holes with scalar hair

We consider the status of black hole (BH) solutions with nontrivial scalar fields but no gauge fields, in four-dimensional asymptotically flat spacetimes, reviewing both classical results and recent developments. We start by providing a simple illustration on the physical difference between BHs in electro-vacuum and scalar-vacuum. Next, we review no-scalar-hair theorems. In particular, we detail an influential theorem by Bekenstein and stress three key assumptions: (1) The type of scalar field equation; (2) the spacetime symmetry inheritance by the scalar field and (3) an energy condition. Then, we list regular (on and outside the horizon), asymptotically flat BH solutions with scalar hair, organizing them by the assumption which is violated in each case and distinguishing primary from secondary hair. We provide a table summary of the state-of-the-art.

Spinning deformations of the D1–D5 system and a geometric resolution of closed timelike curves

Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair (arXiv:1403.2757). These black holes interpolate continuously between the Kerr solution and rotating boson stars in D=4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use.

Flux-branes and the Dielectric Effect in String Theory

Using backwards ray tracing, we study the shadows of Kerr black holes with scalar hair (KBHSH). KBHSH interpolate continuously between Kerr BHs and boson stars (BSs), so we start by investigating the lensing of light due to BSs. Moving from the weak to the strong gravity region, BSs-which by themselves have no shadows-are classified, according to the lensing produced, as (i) noncompact, which yield not multiple images, (ii) compact, which produce an increasing number of Einstein rings and multiple images of the whole celestial sphere, and (iii) ultracompact, which possess light rings, yielding an infinite number of images with (we conjecture) a self-similar structure. The shadows of KBHSH, for Kerr-like horizons and noncompact BS-like hair, are analogous to, but distinguishable from, those of comparable Kerr BHs. But for non-Kerr-like horizons and ultracompact BS-like hair, the shadows of KBHSH are drastically different: novel shapes arise, sizes are considerably smaller, and multiple shadows of a single BH become possible. Thus, KBHSH provide quantitatively and qualitatively new templates for ongoing (and future) very large baseline interferometry observations of BH shadows, such as those of the Event Horizon Telescope.

Stationary metrics and optical Zermelo-Randers-Finsler geometry

The SO(4) isometry of the extreme Reissner–Nordstrom black hole of N = 1, D = 5 supergravity can be partly broken, without breaking any supersymmetry, in two different ways. The “right” solution is a rotating black hole (BMPV); the “left” is interpreted as a black hole in a Godel universe (GBH). In ten dimensions, both spacetimes are described by deformations of the D1–D5pp-wave system with the property that the non-trivial closed timelike curves (CTC’s) of the fivedimensional manifold are absent in the universal covering space of the ten-dimensional manifold. In the decoupling limit, the BMPV deformation is normalizable. It corresponds to the vev of an IR relevant operator of dimension ∆ = 1. The Godel deformation is sub-leading in α � unless we take an infinite vorticity limit; in such case it is a non-normalizable perturbation. It corresponds to the insertion of a vector operator of dimension ∆ = 5. Thus we conclude that from the dual (1 + 1)-CFT viewpoint the SO(4) R-symmetry is broken ‘spontaneously’ in the BMPV case and explicitly in the Godel case.  2003 Elsevier B.V. All rights reserved.

Kerr black holes with Proca hair

Abstract We consider the generalization to String and M-theory of the Melvin solution. These are flux p -branes which have ( p +1)-dimensional Poincare invariance and are associated to an electric ( p +1)-form field strength along their worldvolume. When a stack of D p -branes is placed along the worldvolume of a flux ( p +3)-brane it will expand to a spherical D( p +2)-brane due to the dielectric effect. This provides a new setup to consider the gauge theory/gravity duality. Compactifying M-theory on a circle we find the exact gravity solution of the type IIA theory describing the dielectric expansion of N D4-branes into a spherical bound state of D4–D6-branes, due to the presence of a flux 7-brane. In the decoupling limit, the deformation of the dual field theory associated with the presence of the flux-brane is irrelevant in the UV. We calculate the gravitational radius and energy of the dielectric brane which give, respectively, a prediction for the VEV of scalars and vacuum energy of the dual field theory. Consideration of a spherical D6-brane probe with n units of D4-brane charge in the dielectric brane geometry suggests that the dual theory arises as the Scherk–Schwarz reduction of the M5-branes (2,0) conformal field theory. The probe potential has one minimum placed at the locus of the bulk dielectric brane and another associated to an inner dielectric brane shell.