Rotating black hole with a probe string in Horndeski gravity
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Rotating black hole with a probe string in Horndeski gravity F. F. Santosa Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, Paraíba 58051-970, Brazil Received: 29 May 2020 / Accepted: 24 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we present the effect of a probe string on the complexity of a black hole according to the CA (Complexity equals action) conjecture on Horndeski’s gravity. In our system, we consider a particle moving on the boundary of black hole spacetime in (2 + 1)-dimensions. To obtain a dual description, we need to insertion a fundamental string on the bulk spacetime. The effect of this string is given by the Nambu–Goto term. For the Nambu–Goto term, we can analyze the time development of this system, which is affected by the parameters of Horndeski’s gravity. In our case, we show some interesting complexity properties for this gravity.
1 Introduction Over the past few years, general relativity has been supported by substantial evidence and observations, which have been witnessed in many astrophysical scenarios, these in turn range from Eddington’s measurement of light deflection in 1919 to the recent direct observation of gravitational waves by collaboration LIGO [1,2]. These observational data served as motivation to consider the modified gravity as a theory that has given rich support to phenomenology [3]. However, some problems considered fundamental to be understood in the context of general relativity, such as dark matter, dark energy, and the inflationary phase of the Universe. In recent years, modifications of general relativity have been proposed; however, to carry out such modifications of general relativity, it is necessary to maintain some of its essential properties, which are second-order equations of motion resulting from an invariable action by diffeomorphism and Lorentz’s invariance [4]. By maintaining these properties, additional degrees of freedom of propagation can be added in the gravity sector that is consistent to include additional fields such as scalars, vectors, or tensors. However, to deal with these problems in Einstein’s gravity, one way was to couple the theory with scalar fields. In this sense, these efforts led to the development of the now known Galileo theories, which are theories of scalar tensors [5]. Besides, these studies led to the rediscovery of Horndeski’s gravity [6]. This theory was presented in 1974 by Horndeski for further discussions see [6–9], it is characterized by being a theory of scalar tensors with second-order field equations and second-order energy-moment tensor [4,6,10–13]. The Lagrangian for this theory produces
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second-order equations of motion [10,11,14–22]. This theory also includes four arbitrary functions of the scalar field and its kinetic term. In recent years, the Horndeski
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