We study symmetric teleparallel (STP) gravity model, in which only spacetime non-metricity is nonzero. First we obtain STP equivalent Einstein-Hilbert Lagrangian and give an approach for a generic solution in terms of only metric tensor. Then we obtain a spherically symmetric static solution to the Einstein's equation in STP space-time and discuss the singularities. Finally, we study a model given by a Lagrangian 4-form quadratic in non-metricity. Thus, we seek Schwarzschild-type solutions because of its observational success and obtain some sets of solutions. Finally, we discuss physical relevance of the solutions.
ADAK, MUZAFFER (2006) "The Symmetric Teleparallel Gravity," Turkish Journal of Physics: Vol. 30: No. 5, Article 2. Available at: https://journals.tubitak.gov.tr/physics/vol30/iss5/2