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Dilatonic Black Holes in Higher Curvature String Gravity

P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley

TL;DR

This work shows that in a four-dimensional effective superstring framework with Gauss–Bonnet higher-curvature corrections, black holes can support non-trivial dilaton hair. Through analytic arguments and non-perturbative numerical solutions, it demonstrates that the dilaton hair is of secondary type, tied to the mass, and that the Gauss–Bonnet term enables evasion of the traditional no-hair theorem. The study also uncovers additional finite-energy but non-black-hole solutions and discusses conditions to avoid naked singularities, motivating future stability analyses. Overall, it advances understanding of string-inspired black holes and the role of higher-curvature corrections in gravitational hair structure.

Abstract

We give analytical arguments and demonstrate numerically the existence of black hole solutions of the $4D$ Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of ``secondary" type", in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the ``no-hair" theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.

Dilatonic Black Holes in Higher Curvature String Gravity

TL;DR

This work shows that in a four-dimensional effective superstring framework with Gauss–Bonnet higher-curvature corrections, black holes can support non-trivial dilaton hair. Through analytic arguments and non-perturbative numerical solutions, it demonstrates that the dilaton hair is of secondary type, tied to the mass, and that the Gauss–Bonnet term enables evasion of the traditional no-hair theorem. The study also uncovers additional finite-energy but non-black-hole solutions and discusses conditions to avoid naked singularities, motivating future stability analyses. Overall, it advances understanding of string-inspired black holes and the role of higher-curvature corrections in gravitational hair structure.

Abstract

We give analytical arguments and demonstrate numerically the existence of black hole solutions of the Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of ``secondary" type", in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the ``no-hair" theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.

Paper Structure

This paper contains 7 sections, 60 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Existence of Hair in Gravity with a Gauss-Bonnet term: analytic arguments
  3. Black Hole Solutions
  4. Analytic Solution near the Horizon
  5. Numerical Analysis
  6. Additional Solutions
  7. Conclusions and Outlook

Figures (7)

  • Figure 1: Dilaton field for $r_h=1$ black hole. Each curve corresponds to a different solution characterized by a different initial value of $\phi_h$.
  • Figure 2: Metric components $g_{tt}$ and $g_{rr}$ for $r_h=1$ black hole.
  • Figure 3: Components of the energy-momemtum tensor for $r_h=1$ black hole.
  • Figure 4: Dependence of the dilaton charge $D$ on $M$ and $\phi_\infty$ for the $r_h=1$ black hole. The function $f(M,\phi_\infty)$ stands for the coefficient of $1/r$ in the eq.(\ref{['dm']}).
  • Figure 5: Dilaton field for the singular solution $(66)$. Each curve corresponds to a different solution characterized by a different value of $r_s$ ($r_s= 0.92,0.75,0.62$).
  • ...and 2 more figures