Flávio S. Coelho

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.

Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula.

Recently we estimated the energy radiated in the head-on collision of two equal D-dimensional Aichelburg-Sexl shock waves, for even D, by solving perturbatively, to first order, the Einstein equations in the future of the collision. Here, we report on the solution for the odd D case. After finding the wave forms, we extract the estimated radiated energy for D=5, 7, 9, and 11 and unveil a remarkably simple pattern, given the complexity of the framework: (for all D) the estimated fraction of radiated energy matches the analytic expression 1/2-1/D, within the numerical error (less than 0.1%). Both this fit and the apparent horizon bound converge to 1/2 as D→∞.

Radiation from aD-dimensional collision of shock waves: Higher-order setup and perturbation theory validity

The collision of two D-dimensional, ultra-relativistic particles, described in General Relativity as Aichelberg-Sexl shock waves, is inelastic. In first order perturbation theory, the fraction of the initial centre of mass energy radiated away was recently shown to be 1/2 - 1/D. Here, we extend the formalism to higher orders in perturbation theory, and derive a general expression to extract the inelasticity, valid non-perturbatively, based on the Bondi mass loss formula. Then, to clarify why perturbation theory captures relevant physics of a strong field process in this problem, we provide one variation of the problem where the perturbative framework breaks down: the collision of ultra-relativistic charged particles. The addition of charge, and the associated repulsive nature of the source, originates an extra radiation burst, which we argue to be an artifact of the perturbative framework, veiling the relevant physics.

Relativistic Euler’s three-body problem, optical geometry, and the golden ratio

A Weyl solution describing two Schwarzschild black holes is considered. We focus on the Z{sub 2} invariant solution, with Arnowitt-Deser-Misner mass M{sub ADM}=2M{sub K}, where M{sub K} is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic submanifold. The existence and radii of circular photon orbits in this submanifold are studied, as functions of the distance 2L between the two black holes. For L{yields}0 there are two such orbits, corresponding to r=3M{sub ADM} and r=2M{sub ADM} in Schwarzschild coordinates. As the distance increases, it is shown that the two photon orbits approach one another and merge when M{sub K}={phi}L, where {phi} is the golden ratio. Beyond this distance there exist no circular photon orbits. The two null orbits delimit a forbidden band for timelike circular orbits, which is interpreted in terms of optical geometry. For large L, timelike circular orbits are allowed everywhere, as in the analogous Newtonian problem. The analysis is generalized by considering a Z{sub 2} invariant Weyl solution with an array of N black holes and also by charging the black holes, which connects the Weyl solution to a Majumdar-Papapetrou spacetime.

RADIATION FROM A D-DIMENSIONAL COLLISION OF SHOCK WAVES: AN INSIGHT ALLOWED BY THE D PARAMETER

We consider the radiation emitted in a collision of shock waves, in D-dimensional General Relativity (GR), and describe a remarkably simple pattern, hinting at a more fundamental structure, unveiled by the introduction of the parameter D.

On the scalar graviton in n-DBI gravity

n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac’s theory of constrained systems. Firstly, studying scalar perturbations around Minkowski spacetime, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Hoyrava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.

n-DBI gravity, maximal slicing, and the Kerr geometry

Recently, Herdeiro et al. [Phys. Rev. D 84, 124048 (2011)] have established that solutions of Einsteins gravity admitting foliations with a certain geometric condition are also solutions of

Radiation from a D-dimensional collision of shock waves: proof of first order formula and angular factorisation at all orders

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Radiation from a D-Dimensional Collision of Shock Waves: A Summary of the First Order Results

-DBI gravity, Herdeiro and Hirano [J. Cosmol. Astropart. Phys. 05 (2012) 031]. Here we observe that, in vacuum, the required geometric condition is fulfilled by the well known maximal slicing, often used in numerical relativity. As a corollary, we establish that the Kerr geometry is a solution of

Radiation from a D-Dimensional Collision of Shock Waves: Numerics and a Charged Case

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