On the motion of hairy black holes in Einstein-Maxwell-dilaton theories

Abstract

Starting from the static, spherically symmetric black hole solutions in massless Einstein-Maxwelldilaton (EMD) theories, we build a "skeleton" action, that is, we phenomenologically replace black holes by an appropriate effective point particle action, which is well suited to the formal treatment of the many-body problem in EMD theories. We find that, depending crucially on the value of their scalar cosmological environment, black holes can undergo steep "scalarization" transitions, inducing large deviations to the general relativistic two-body dynamics, as shown, for example, when computing the first post-Keplerian Lagrangian of EMD theories.1 Note that a = 0 reduces to Einstein-Maxwell theory minimally coupled to a scalar field, while a = 0 is motivated by low-energy limits of string theory, see, e.g., [18]; a = √ 3 is equivalent to the dimensional reduction of the Kaluza-Klein theory [19] [20].

Post-Newtonian dynamics and black hole thermodynamics in Einstein-scalar-Gauss-Bonnet gravity

“…The question we address here is the calculation of the function m A (ϕ) for EsGB BHs. Following the techniques developed in [27], we impose that the fields generated by extremizing the action (III.1) match those of the BH built in the previous section.…”

“…We improve on that treatment in two ways: (1) we allow for the fact that the BH masses and scalar "charges" are not constant: instead, we consistently skeletonize the BHs following a well-established procedure first introduced by Eardley in scalar-tensor gravity [26], and recently generalized to Einstein-Maxwell-dilaton theory by one of us [27,28]; (2) as a consequence of the skeletonization, we can self-consistently compute higher-order post-Newtonian (PN) terms in the Lagrangian.…”

Maxwell-dilaton dynamics

“…The model studied here results from restricting to flat-space and U(1) abelian gauge field [3]. If one instead allows for curved space, one has the Einstein-Maxwell-Dilaton model studied recently [4][5][6][7][8][9][10][11][12]. Understanding the dynamics of this simpler system may help elucidate aspects of the more general system.…”

Gravitational radiation from compact binary systems in Einstein-Maxwell-dilaton theories

“…The "sensitivities" being known, all the body-dependent quantities (5) are known for a given black hole A, that is, for given values of (q A , µ A ), as functions of ϕ 0 . In particular, as highlighted in [1], we have that α 0 A ≡ α A (ϕ 0 ) (which is an exact "Fermi-Dirac distribution" when a = 1) transitions from zero (Schwarzschild limit, with β 0 A → 0 and e 2 A → 0) to a (fully scalarized black hole, with β 0 A → 0 and e 2 A → 1 + a 2 ) when the scalar cosmological background ϕ 0 increases.…”

“…In [1], we solved the field equations (3,4) perturbatively around a flat, Minkowski background η µν and the constant value ϕ 0 of the scalar field at infinity, which is imposed by the cosmological environment of the binary system. We then derived the two-body Lagrangian, at post-keplerian order (1PK) and in harmonic coordinates, which generalizes that of Einstein, Hilbert and Hoffman in general relativity.…”