Arnold Schwarzenegger has given his lovechild a furnished home gymnasium for his birthday. The film star has presented his son Joesph, who he fathered during his affair with the family's former housekeeper Mildred Baena, with hi-tech exercise equipment for his 16th birthday, according to editors at TMZ.com. The Terminator actor confessed his fling with Baena in 2011 and has since reportedly built a close relationship with Joseph, even flying him to several movie premieres. A source tells TMZ, "Once the truth came out, Arnold embraced Joseph. Since then, they've been slowly building a great relationship."